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Estimation Based on Nearest Neighbor Matching: From Density Ratio to Average Treatment Effect

Journal: Econometrica

Date: 20231101

Author: Lin, Zhexiao; Ding, Peng; Han, Fang

Abstract:
Nearest neighbor (NN) matching is widely used in observational studies for causal effects. Abadie and Imbens (2006) provided the first large-sample analysis of NN matching. Their theory focuses on the case with the number of NNs, M fixed. We reveal something new out of their study and show that once allowing M to diverge with the sample size an intrinsic statistic in their analysis constitutes a consistent estimator of the density ratio with regard to covariates across the treated and control groups. Consequently, with a diverging M, the NN matching with Abadie and Imbens' (2011) bias correction yields a doubly robust estimator of the average treatment effect and is semiparametrically efficient if the density functions are sufficiently smooth and the outcome model is consistently estimated. It can thus be viewed as a precursor of the double machine learning estimators.

Link: Google Scholar

Key Findings

Nearest Neighbor Matching Efficiency

When the number of nearest neighbors (M) is allowed to diverge with sample size, the matching estimator achieves semiparametric efficiency and double robustness for estimating average treatment effects.

Computational Advantage

The proposed nearest neighbor matching method provides computationally efficient estimation with subquadratic time complexity while maintaining statistical optimality.

Bias Correction Performance

Bias-corrected matching estimators demonstrate strong empirical performance across different sample sizes and matching specifications, with coverage rates close to nominal levels.

Treatment Effect Estimation Performance

  • Root Mean Squared Error (RMSE) decreases consistently as sample size increases
  • Performance improves with larger sample sizes across all matching specifications
  • Diverging M shows better performance compared to fixed M values

Coverage Rate Performance

  • 95% coverage rates approach nominal level as sample size increases
  • Both SE and AISE methods provide reliable confidence intervals
  • Coverage performance is robust across different M specifications

Computational Efficiency Analysis

  • Bias decreases with increasing sample size
  • Diverging M specifications show minimal bias
  • Computational efficiency maintained with larger samples

Contribution and Implications

  • Provides theoretical justification for using diverging number of matches in nearest neighbor matching
  • Demonstrates computational efficiency while maintaining statistical optimality
  • Bridges gap between matching methods and modern machine learning approaches
  • Offers practical guidance for implementing matching estimators in large-scale studies

Data Sources

  • RMSE Chart: Constructed using data from Table I of the article, showing root-mean-squared-error values for different sample sizes and matching specifications
  • Coverage Rate Chart: Based on Table I's 95% coverage rates for both SE and AISE methods
  • Bias Chart: Derived from the bias columns in Table I, showing absolute bias values across sample sizes